Crossland Criterion Research Articles

Fatigue prediction and optimization of laser peened turbine blade using artificial neural networks and ANFIS

AbstractThis paper investigates the fatigue behavior prediction of Ti‐6Al‐4V thin‐leading‐edge turbine blade specimens treated with laser shock peening (LSP) using two advanced artificial intelligence (AI) methods: artificial neural networks (ANNs) and adaptive network‐based fuzzy inference system (ANFIS). The study aims to estimate the endurance under high cycle loading conditions. First, using ABAQUS and MATLAB software, the modified Crossland criterion for uniaxial loading is applied to recalibrate endurance limit values based on modifications induced by the LSP process. Then, these techniques are employed to predict the modified Crossland criterion profile and endurance limit values influenced by the LSP treatment. Specifically, numerical values are used as training and testing data for these AI models. As a result, these AI methods provide highly accurate prediction and optimization of the modified Crossland criterion and endurance limits, demonstrating their reliability and effectiveness.

Numerical investigation of the influence of defects on the multiaxial fatigue strength of additively manufactured alloys

Laser Powder Bed Fusion (L-PBF) is one of the Additive Manufacturing (AM) techniques that have revealed salient advantages in enabling the fabrication of 3D parts with intricate shapes and added functionalities. Despite many advances, scientific challenges still exist. One of them, especially where the additively manufactured industrial components undergo fatigue loading, is the defects (gas pores and Lack of Fusions (LoFs)) that are induced during the fabrication process. The present work aims to investigate the influence of AM defects on fatigue strength under multiaxial loading conditions. From numerical simulations, the key question addressed is the impact of defects’ morphology on their criticality under multiaxial loadings. Finite Element (FE) elastic simulations at load ratio R = -1 under multiaxial loading conditions (tension, torsion and tension-torsion) have been performed on numerically generated spherical defect and LoFs obtained from micro-CT scans of additively manufactured TA64 alloy. The Crossland criterion (stress-based) was used to evaluate the fatigue strength and the obtained numerical results were compared with the available experimental results.

Fatigue life prediction of the nitrided steel by multiaxial high cycle fatigue criteria

The present study aims to predict the fatigue strength of ion-nitrided 42CrMo4 steel, using multiaxial high cycle fatigue (HCF) criteria and considering the effects of stabilized residual stresses and surface hardening. The predicted fatigue strength was compared to experimental data obtained after three-points bending fatigue tests at two stress ratios (0.1 and 0.5) and for notched (Kt = 1.6) nitrided and untreated specimens. A 3D finite element (FE) model of a three-point bending fatigue test was developed under ABAQUS software in order to determine the actual applied cyclic stress state at the notch. The results show that ion-nitriding treatment led to 32% improvement in the fatigue strength at 106 cycles compared to the untreated material. This improvement is explained by the advantageous effect of ion-nitriding treatment in terms of compressive residual stresses and surface layer hardening. Both stabilized residual stress state and hardening effects were successfully implemented into various multi-axial HCF criteria, including Sines, Crossland, Dang Van and Matake criteria. A sensitivity analysis has shown that Crossland criterion has permitted to predict the fatigue limits in accordance with the experimental results.

Reliability prediction of high‐cycle fatigue behavior of parts treated by laser shock peening

AbstractThe purpose of this paper is to develop a global approach to predict the reliability of the high‐cycle fatigue behavior of mechanical components treated by laser shock peening (LSP). Most works that exist in the literature have introduced experimental and numerical studies. The originality of our investigation is to predict and validate the reliability of high‐cycle fatigue of the workpieces treated by LSP treatment by using the modified Crossland criterion. Based on previous works made by our team that shows the finite element simulation of the LSP process, this approach will be based on the integration of probabilistic fatigue criteria adapted to the superficially treated parts using ABAQUS software. After the validation of this approach, it will allow design engineers to optimize the operating conditions of the LSP process.

Modelling of critical defect distributions for estimating the size effect of selective laser melted 316L stainless steel

The paper presents modelling the effect of specimen size on the fatigue behaviour of SLM 316L stainless steel. The failure mechanism assumes an important role in fatigue crack initiated from random material defects. The finite element calculations showed an increase in the non-local stress distribution of the Crossland criterion for varying defect location and size. A procedure for generating critical defects in a highly stressed volume is proposed to simulate the distributions of extreme values of equivalent stress and material sensitivity coefficient for size effect. The predicted fatigue strength for selected defect size distribution parameters correlates well with experimental data.

On the high cycle fatigue resistance of austenitic stainless steels with surface gradient microstructures: Effect of load ratio and associated residual stress modification

The effect of gradient microstructure generated by ultrasonic surface mechanical attrition treatment (SMAT) on the fatigue performance of an austenitic stainless steel has been evaluated in the context of localized and general plasticity by comparing two load ratios: fully reversed tension-compression (TC) RTC = -1 and tension-tension (TT) RTT = +0.1, respectively.After identical SMAT processing conditions, the fatigue limit was enhanced by +17% for RTC while it was reduced by -7% for RTT. Under RTC cyclic loading, self-heating of the specimens and sub-surface martensitic transformation occurred but not for RTT. The residual stress measurements have also revealed that while the stress gradient was smoothed after the RTC fatigue loading, it was completely reverted for the RTT one. In turns, the fatigue crack initiation sites and propagation were modified between the RTC and RTT loading conditions.Considering the stabilized surface residual stress after fatigue loading, the use of a Crossland criterion allowed to explain both the effects of load ratio and SMAT on the high cycle fatigue behavior of the stainless steel. It turns out that under the studied loading conditions the modifications of residual stress state can be considered as the primary factor governing the varying fatigue performances and the observed triggering at different initiation sites.

Fatigue strength evaluation and lifetime estimation for ductile cast irons under multiaxial loading

The goal of the present research is to theoretically estimate both fatigue strength and lifetime of Ductile Cast Iron (DCI) smooth specimens under uniaxial and biaxial cyclic loading. To such an aim, a critical plane-based multiaxial fatigue criterion formulated in terms of stresses is hereafter applied to several experimental fatigue data available in the technical literature, related to both infinite and finite life tests. The theoretical results (in terms of fatigue strength and fatigue life) are compared with the experimental ones and, for finite life fatigue tests, also with those derived through the Crossland criterion.

Investigation of the sensitivity of the fatigue resistance to defect position in aluminium alloys obtained by Selective laser melting using artificial defects

This study focuses on the influence of defects on the fatigue behavior of AlSi7Mg0.6 alloy produced by Selective laser melting. Artificial defects were generated in fatigue specimens by introducing holes in the CAD files prior manufacturing. The introduction of such defects, whose sizes and positions are controlled, aims to provide a proper assessment of defect sensitivity, in particular regarding the influence of defect position. Fatigue tests were performed, and finite-element calculations accounting for real defect geometries were conducted. The criticalities of the simulated defects were then evaluated using a non-local Crossland criterion, and discussed with regard to the experimental results.

Fatigue strength prediction methodology of shot-peened materials

Shot peening is used to enhance fatigue strength, but it is usually neglected by manufacturing design. The main purpose of the present work is to suggest strategies capable of making connection between the process conditions and the fatigue strength. In the present paper, fatigue lives of shot-peened parts were predicted. A new multiaxial HCF model, based on the Crossland criterion, was proposed; it integrates the favourable effects of shot peening that are the combined effect of compressive residual stresses and strain hardening. The plastic strain field accounts for the strain hardening. In order to compute residual stress and equivalent plastic strain profiles due to the repeated impacts, we have modelled and simulated, through a finite element method, the impact of the shot dynamics resulting from the process. The relaxation of induced compressive residual stresses, over the fatigue life, has been considered. For the purpose of spotlighting the capability of the present methodology, the predictions were compared with existing experimental data. This study demonstrates that the single effect of stabilized residual stress is not sufficient to explain the full enhancement of fatigue resistance. The proposed fatigue criterion provides a conservative prediction in terms of endurance limit.

Topology optimization of the multi-fasteners jointed structure considering joint load constraint and fatigue constraints

The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q - p relaxation is used and p ≥ q ≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.

Fatigue limit assessment for defective materials based on affected depth

In this study, a new fatigue limit assessment of defective materials submitted to acyclic loading is presented. This assessment is based on the analysis of the stress distribution in the vicinity of the defect. The defect shapes are reduced to a semi-spherical or semi-elliptical void at the surface of a sample subjected to a fatigue loading. The Finite Element (FE) solutions are generated to assess the stress field around the defect. The Crossland equivalent stress is used to analyse the stress distribution close to the defect. From this analysis, an affected depth is defined as the depth from the tip of the defect to the interior of the sample in which the Crossland criterion is violated. For a load close to the fatigue limit and for each defect size, we find that the affected depth is almost constant.Using the concept of the affected depth, a fatigue limit assessment model dedicated for defective material is proposed. This model is applied for two defective materials under different loading paths. Results are in good agreement with the experimental investigations and confirm that the proposed parameter − affected depth– can properly characterise the influence of the shape and the size of the defect on the fatigue behaviour under different loading paths.

Predicting the effects of material properties gradient and residual stresses on the bending fatigue strength of induction hardened aeronautical gears

This paper proposes an experimental methodology to characterize complex parts presenting various gradients using aeronautical induction surface hardened spur gears. A 3D fatigue model taking into account residual stresses, microstructure variations, and surface roughness is then proposed for the prediction of the bending endurance limit. The model is based on the well-known Crossland criterion; calibrated with representative axial and torsion laboratory specimens. The results are compared with testing performed on a custom-made single tooth bending fatigue (STBF) rig. Fracture surface analysis using electronic microscopy is used to investigate the crack initiation sites. It is shown that residual stresses can have a significant impact on bending fatigue and that two induction treatments can present very different fatigue resistance even if the shape and depth of the hardened layer is identical in the root. The proposed methodology could be adapted to other geometries and surface treatments.

Multi-axial Fatigue Criteria with Length Scale and Gradient Effects

The objective of the work is first to extend some classic high cycle fatigue (HCF) criteria (as Crossland, Dang Van, Papadopoulos, ...) to take into account a sensitivity of the criteria to stress spatial variations occurring at length scale lg, and second to compare the performances of the extensions through numerical simulations of experimental fatigue tests. After an introduction of the basic criteria and their gradient based extensions proposed by Luu et al., we focus on the Crossland criterion to propose a more practical and simple expression taking into account the gradient of the stress amplitude and the maximum hydrostatic stress. The proposition is then tested and applied to different simple situations: 4-point bending and cantilever rotative bending. The relative errors between the exact solutions and the numerical simulations are estimated. Biaxial bending-torsion tests are also simulated to demonstrate the capabilities of the approach. The generalization of the approach to other multiaxial fatigue criteria is briefly shown through the case of Papadopoulos 2001 proposal. Finally, the present study develops a simple formulation of gradient multi-axial fatigue criteria extending the classical HCF criteria. In this work only stress gradient with a beneficial effect on fatigue have been considered.

Multiaxial fatigue design of cast parts: Influence of complex defect on cast AS7G06-T6

AS7G06-T6 cast aluminum alloy is tested under tension, torsion and tension–torsion fatigue loading for two load ratios. Basquin’s law and step loading method are used to obtain the fatigue limit under multiaxial loading. Crossland criterion and principal stress criterion considering Goodman idea are compared to evaluate the multiaxial behavior. The influence of complex defects on fatigue limit is analyzed under multiaxial loadings. Several artificial defects are machined on fatigue specimen with different distance between edges. A new definition of the equivalent defect size considering the distance between defect edges is proposed. For both tension and tension–torsion fatigue, the competition between single natural defect and complex artificial defects is observed and analyzed.

Influence of complex defect on cast AS7G06-T6 under multiaxial fatigue loading

AS7G06-T6 cast aluminum alloy is tested under tension, torsion and tension–torsion fatigue loading for two load ratios. Basquin’s law and step loading method are used to obtain the fatigue limit under multiaxial loading. Crossland criterion and principal stress criterion considering Goodman idea are compared to evaluate the multiaxial behavior. The influence of complex defects on fatigue limit is analyzed under multiaxial loadings. Several artificial defects are machined on fatigue specimen with different distance between edges. A new definition of the equivalent defect size considering the distance between defect edges is proposed. For both tension and tension–torsion fatigue, the competition between single natural defect and complex artificial defects is observed and analyzed.

Evaluation of Estimation Models for Multiaxial Fatigue Life

Some of estimation models for multiaxial fatigue are reviewed. They are the high cycle fatigue (HCF) estimation models based on the Crossland criterion, the Papadopoulos criterion, the Findley criterion, the Matake criterion and the McMiarmid criterion, and the low cycle fatigue (LCF) estimation models based on the Brown and Miller, FS, and SWT parameters, respectively. The HCF estimation models are checked against the experimental data of 30NCD16 steel under fully reversed bending, fully reversed torsion, bending or tension with mean normal stress, multiaxial loading condition. Their fatigue life correlation for the fully reversed torsion tests falls within about 5% for the average absolute value of relative errors. The estimation model based on the Matake criterion can be suitable for all the loading conditions for 30NCD16 steel, its predicted lives fall within the factor three bandwidth. The LCF estimation models are evaluated by the experimental data of 1050 steel under normalized, quenched and tempered, and induction hardened conditions. For 90° out‐of‐phase loading conditions, the predicted lives by the SWT estimation model scatter within the factor three bandwidth for 1050 steel under normalized and quenched and tempered conditions. The average absolute values of estimated errors by the SWT and Brown–Miller estimation models are 10.5 and 11.5%, respectively, for quenched and tempered 1050 steel under in‐phase loading conditions.

The Mobility of Principal Stress Directions in Crossland Criterion

This paper is a new proposal of a multiaxial fatigue criterion which takes better into account the mobility of principal directions of stress tensor. The model proposed is based on the Crosland Criterion and start by defining an equivalent stress with zero out- of-phase angles for the stress components with a phase difference, which apply to Crossland criterion gives the Crossland* criterion. Poor predictions are obtained from Crossland criterion for stress states with mobile principal stress directions. We impute this discrepancy not on the capacity of parameters appearing in the criterion to account for the complexity of the loading or to account the additional damage generate by the mobility of principal stress directions, but instead on the procedure of evaluation of parameters appearing in the criterion and also on the formulation of linear combinations of two scalar parameters proposed by Crossland. Assuming that the second invariant of the stress deviator and maximum hydrostatic pressure can account of the additional damage generate by the mobility of principal stress directions.The re-formulated Crossland criterion gives good predictions of experimental data when stress states present mobility of principal stress directions. The results show that the predictions obtained using in general the equivalent stress should be more satisfactory than the initial Crossland criterion and Crossland.

Influence of the rheological behaviour of the lubricant on the appearance of pitting in elastohydrodynamic regime

ABSTRACTThis paper analyses the influence of lubricant behaviour on the appearance of pitting. It attempts to study the effect of viscosity–pressure relation, compressibility, film thickness–roughness relation and friction coefficient on pitting failure of the contacting elements. To explain these effects, we first deal with the influence of the oil on the lubrication of the contact using elastohydrodynamic theory and secondly two multiaxial fatigue criteria are used, Crossland criterion and Dang Van criterion, to evaluate the influence of the rheology on the appearance of pitting. Finally, different applications are presented together with a discussion on the results obtained.

A non-local fatigue approach to quantify Ti–10V–2Fe–3Al fretting cracking process: Application to grinding and shot peening

This paper presents an experimental study on the tribological behaviour and cracking response of a Ti–10V–2Fe–3Al titanium alloy under fretting loading with a cylinder on plane configuration. Three types of surfaces were investigated: a polished one considered as the reference, a ground one and a shot peened surface. Surfaces were compared with respect to residual stress, hardness and roughness. The first step of this study was to determine sliding conditions and coefficient of friction of the three contact types. Next, fretting tests under stabilized partial slip regime were carried out to investigate crack nucleation and propagation. Results show that whatever surface roughness or residual stress in the material, tribological behaviour is the same. These latter confirm that sliding condition and coefficient of friction in partial slip regime is due to material effect and not to roughness or surface hardness. Then, residual stress induced by grinding or shot peening have no influence on the crack nucleation threshold under fretting solicitation because crack nucleation is only induced by a sufficient tangential loading. The crack nucleation threshold is formalized by applying the Crossland criterion taking into account the stress gradient and the ensuing “size effect”. As expected, cracks propagation is influenced by residual stress under the surface. Compared to the reference case, for a same loading parameters set, residual stress induced by grinding is not sufficient to decrease the crack length reached whereas effects of shot peening decrease highly these latter. So, there is a threshold of residual stress from which residual stresses are useful against cracking.

Probabilistic prediction of high cycle fatigue reliability of high strength steel butt‐welded joints

ABSTRACTThe aim of this paper is to develop a probabilistic approach of high cycle fatigue (HCF) behaviour prediction of welded joints taking into account the surface modifications induced by welding and the post‐welding shot peening treatment. In this work, the HCF Crossland criterion has been used and adopted to the case of welded and shot peened welded parts, by taking into account the surface modifications which are classified as follows: (i) the compressive residual stresses, (ii) the surface work‐hardening, (iii) the geometrical irregularities and (iv) the superficial defects. The random effects due to the dispersions of: (i) the HCF Crossland criterion material characteristics (ii) the applied loading and (iii) the surface modifications parameters are introduced in the proposed model. The HCF reliability has been computed by using the ‘strength load’ method with Monte Carlo simulation. The reliability computation results lead to obtain interesting and useful iso‐probabilistic Crossland diagrams (PCD) for different welding and shot peening surface conditions. To validate the proposed method, the approach has been applied to a butt‐welded joint made of S550MC high strength steel (HSS). Four types of specimens are investigated: (i) base metal (BM), (ii) machined and grooved (MG) condition, (iii) As welded (AW) condition and (iv) as welded and shot peened (AWSP) condition. The comparison between the computed reliabilities and the experimental investigations reveals good agreement leading to validate the proposed approach. The effects of the different welded and post‐weld shot peened specimen's surface properties are analysed and discussed using the design of experiments (DoE) techniques.